Highly Efficient Coupling of Nanolight Emitters to a Ultra-Wide Tunable Nanofibre Cavity

Solid-state microcavities combining ultra-small mode volume, wide-range resonance frequency tuning, as well as lossless coupling to a single mode fibre are integral tools for nanophotonics and quantum networks. We developed an integrated system providing all of these three indispensable properties. It consists of a nanofibre Bragg cavity (NFBC) with the mode volume of under 1 μm3 and repeatable tuning capability over more than 20 nm at visible wavelengths. In order to demonstrate quantum light-matter interaction, we establish coupling of quantum dots to our tunable NFBC and achieve an emission enhancement by a factor of 2.7.

grooves are milled from one side, resulting in an arch-like shape. Their depth is 45 nm. To yield a Bragg grating with a design wavelength of 630 nm, the spatial period of the grooves Λ B is adjusted according to the Bragg formula: where n ef f is the effective refractive index of the nanofibre. Putting in the calculated effective index n ef f =1.07 for the wavelength of 630 nm and the fibre diameter of 300 nm, the grating period Λ B is determined to be 300 nm. The grooves achieve a large refractive index modulation ∆n of ∼ 0.066 as calculated via finite difference time domain simulations. In the middle of the Bragg grating, a defect of 3 2 Λ B is introduced in order to form the cavity. The resulting structure is shown in Figure 1a

Simulation of the coupling efficiency
The coupling efficiencies to a fundamental mode of the fibre are calculated based on our recent paper. 1 Figure 2 shows the geometry used for the simulation. The dipoles are placed at weak and strong points of the electric field inside the cavity. The direction of the dipoles is the X-axis. The wavelength of the dipoles is set to the resonance of the NFBC (634.32 nm).
The coupling efficiencies for one end of the fibre are monitored at 28 µm away from the centre of the simulation region and then summed up for the total coupling efficiency.  Table 1 shows the calculation results for the cases where a single dipole is located at the corresponding position. When the dipole is placed at positions with a weak electric field (a and b), the coupling efficiency is very low. In contrast, when the dipole is placed at positions with a strong electric field (c and d), the coupling efficiency is over 0.8.

Purcell formula and broad band emitters
Coupling of emitters to optical cavities results in a coupled system with new properties. In the so called weak coupling limit, where dissipation is dominating, this leads to an enhancement of the emitter's emission rate via the Purcell effect. 2 The emission enhancement factor is given by the Purcell formula: with λ being the free space emission wavelength of the emitter, n the refractive index, Q the quality factor of the cavity, and V its mode volume.
For a broad band emitter, where only parts of the emission spectrum are inside the cavities resonance, the situation is more difficult. Only a part of the decay channels get enhanced by the factor P . In the emitters spectrum, the relative strength of the emission at one wavelength λ ′ in a spatial mode m I λ ′ ,m is: where k λ , n are the decay rates for transitions at the wavelengths λ into mode n and k nr is the non radiative decay rate. Sorting the decay rated at different wavelengths and modes into the ones that will be affected by the cavity k cav and the unaffected ones k f ree results in: where we have introduced I cav as the relative intensity of the part of the spectrum, which will be affected by the cavity. When coupling to the cavity, the rate k cav gets enhanced by the Purcell factor P resulting in an enhanced emission into the cavity I enh : For situations, where decay into other channels dominates over the enhanced decay into the cavity as it is the case for our experiment, the denominator of Equation 5 can be assumed to be constant, leading to a direct connection of Purcell factor and emission enhancement:    Figure 4: Fluorescence spectra of a single quantum dots (QDs) coupled to a nanofibre cavity. Panels a,b,c, show the detected spectra in confocal configuration and at the fibre's ends. The measured data is shown in black and a a Gaussian energy distribution fitted to the confocal measurementsis shown in red. In green the corresponding cavity resonance is shown. An enhancement of the single QD's fluorescence is visible at the resonance wavelength as well as strong suppression in the Bragg mirrors' band gap. This behaviour indicated that the QD's spatial position is not exactly at the cavity, but slightly shifted towards one of the mirrors. In d a time trace of the QD's emission as collected through the fibre is shown. A clear two-level blinking indicates the presence of a single quantum emitter.

Tuning at cryogenic temperatures
In order to get to the single-emitter regime -the regime needed, for example, for efficient single photon sources -we bleach the emission from the quantum dots with the excitation laser until the emission is considerably darker. The resulting emission spectrum is shown in Figure 4. While the main features are similar to the case of a few QDs, the enhancement is less pronounced while the emission inhibition inside the band gap is larger. This means that in the bleaching process a QD survived that is not perfectly coupled. On the other hand, this also means that coupling for the now bleached particles was even better than calculated.
To prove the single emitter character of the remaining quantum dot, we look at its blinking